# How to calculate ring strain energy?

Series A and B below can be viewed in two different ways to annulate an ethano-bridge onto four-, five-, and six-membered rings. Using the $$\Delta_\mathrm{f}H^\circ$$ values given (in kcal/mol), how can one calculate the strain energy for each compound?

Could anyone also explain whether the trend seen in each series is consistent with expectations based on additivity of ring strain?

Typically, ring strain energies (RSE) are calculated as the difference of the heat of formation of cyclic starting materials and less cyclic products in homodesmic reactions.

For cyclopropane, the RSE would be calculated using the following reaction:

$$\ce{(CH2)3 + 3 CH3-CH3 -> 3 CH3-CH2-CH3}$$

• It's called hypohomodesmotic or HD1, and is a subset of the isodesmic reaction. It describes the same amount of carbons in the their various states of hybridization on reactant and product side, and same amount of carbon atom with 0,1,2,3 hydrogens attached. However, it is not a Homodesmotic reaction (HD2) since the carbon-carbon bond hybridization of reactant and product is not balanced. spa-sp3, sp2-sp3 etc.
– user9596
Nov 2, 2014 at 1:39

I ran out of space in the comment...to the comment (user9596)...to Klaus' answer.

Klaus is right. The example with cyclopropane is certainly homodesmotic (HD2). In my opinion, this should now be called RC4 based on a new scheme in a 2009 paper by Wheeler Houk, Schleyer and Allen. You may reference http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2711007/

Criteria for HD1: (a) equal numbers of carbon atoms in their various states of hybridization in reactants and products, and (b) a matching of carbon-hydrogen bonds in terms of the number of hydrogen atoms joined to individual carbon atoms in reactants and products.

OK, so the criteria for HD1 are satisfied.

Criteria for HD2: (a) equal numbers of each type of carbon-carbon bond [Csp3–Csp3, Csp2–Csp3, Csp2–Csp2, Csp2=Csp2 etc.] in reactants and products, and (b) equal numbers of each type of carbon atom (sp3, sp2, sp) with zero, one, two, and three hydrogens attached in reactants and products.

It turns out that the criteria for HD2 are satisfied as well.

As a last bit, here are the (very similar) criteria for RC4: (a) equal numbers of each type of carbon-carbon bond [Csp3–Csp3, Csp3–Csp2, Csp3–Csp, Csp2–Csp2, Csp2–Csp, Csp–Csp, Csp2=Csp2, Csp2=Csp, Csp=Csp, Csp≡Csp] in reactants and products, and (b) equal numbers of each type of carbon atom (sp3, sp2, sp) with zero, one, two, and three hydrogens attached in reactants and products.